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A100452 Triangle read by rows, based on array described below. 5
1, 3, 4, 7, 8, 9, 13, 14, 15, 16, 19, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 39, 40, 42, 44, 45, 48, 49, 49, 50, 51, 52, 55, 60, 63, 64, 63, 64, 66, 68, 70, 72, 77, 80, 81, 79, 80, 81, 84, 85, 90, 91, 96, 99, 100, 91, 92, 93, 96, 100, 102, 105, 112, 117, 120 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Form an array a(m,n) (n >= 1, 1 <= m <= n) by: a(1,n) = n^2 for all n; a(m+1,n) = (n-m)*floor( (a(m,n)-1)/(n-m) ) for 1 <= m <= n-1.

The interesting property of this array is that the main diagonal gives A000960.

LINKS

Table of n, a(n) for n=1..65.

H. Killingbergtro and C. U. Jensen, Problem 116, Nord. Mat. Tidskr. 5 (1957), 160-161.

EXAMPLE

Array begins:

  1 4 9 16 25 36 49 64 81 100 ...

    3 8 15 24 35 48 63 80  99 ...

      7 14 21 32 45 60 77  96 ...

        13 20 30 44 55 72  91 ...

           19 28 42 52 70  90 ...

and triangle begins:

   1

   3  4

   7  8  9

  13 14 15 16

  19 20 21 24 25

  27 28 30 32 35 36

  ...

MATHEMATICA

max = 11; a[1, n_] := n^2; a[m_, n_] /; 1 < m <= n := a[m, n] = (n-m+1)*Floor@((a[m-1, n] - 1)/(n-m+1)); a[_, _] = 0; t = Table[ a[m, n], {m, 1, max}, {n, m, max}]; Flatten[ Table[ t[[m-n+1, n]], {m, 1, max}, {n, 1, m}]] (* Jean-Fran├žois Alcover, Feb 21 2012 *)

CROSSREFS

Cf. A000960, A100453. Row 1 = squares, row 2 = squares - 1, row 3 = A100451. Column sums give A100454.

See also A100461.

Sequence in context: A154366 A226227 A319736 * A004201 A109054 A129142

Adjacent sequences:  A100449 A100450 A100451 * A100453 A100454 A100455

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane, Nov 22 2004

STATUS

approved

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Last modified November 20 18:16 EST 2019. Contains 329337 sequences. (Running on oeis4.)